Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to b...Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to be a bialgebra are proved. Then, B#^τδH is a coquasitriangular Hopf algebra under certain conditions. This coquasitriangular Hopf algerbra generalizes some known cross products. Finally, as an application, an explicit example is given.展开更多
In this paper,we show that if H is a finite dimensional Hopf algebra then H is quasitri-angular if and only if H is coquasi-triangular. As a consequentility ,we obtain a generalized result of Sauchenburg.
We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diago...We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).展开更多
文摘Let H be a Hopf algebra and B an algebra with two linear maps δ, τ： H H→B. The necessary and sufficient conditions for the twisted crossed product B#^τδH equipped with the tensor product coalgebra structure to be a bialgebra are proved. Then, B#^τδH is a coquasitriangular Hopf algebra under certain conditions. This coquasitriangular Hopf algerbra generalizes some known cross products. Finally, as an application, an explicit example is given.
基金Partially supported by the National Natural Science Foundation of China.
文摘In this paper,we show that if H is a finite dimensional Hopf algebra then H is quasitri-angular if and only if H is coquasi-triangular. As a consequentility ,we obtain a generalized result of Sauchenburg.
基金supported by National Natural Science Foundation of China(Grant No.11371290)
文摘We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).
